Generalized spring tensor models for protein fluctuation dynamics and conformation changes

In the last decade, various coarse-grained elastic network models have been developed to study the large-scale motions of proteins and protein complexes where computer simulations using detailed all-atom models are not feasible. Among these models, the Gaussian network model (GNM) and anisotropic network model (ANM) have been widely used. Both models have strengths and limitations. GNM can predict the relative magnitudes of the fluctuations well, but due to its isotropic assumption, it can not be applied to predict the directions of the fluctuations. In contrast, ANM adds the ability to do the latter, but it loses a significant amount of precision in the prediction of the magnitudes. In this article, we develop a generalized spring tensor model (STeM) that is able to predict well both the magnitudes and the directions of the fluctuations. STeM also outperforms ANM in explaining protein conformation changes. All of these are accomplished without sacrificing the essential features that have made ANM and GNM attractive.